Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds

“No free lunch” results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling, which is more or less realistic for a given problem. Some models are “expensive” (strong assumptions, such as sub-Gaussian tails), others are “...

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Autores principales:	Benjamin Guedj, Louis Pujol
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	statistical learning theory PAC-Bayes theory no free lunch theorems Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/60e63bead773480ead8e98baa4144956
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id	oai:doaj.org-article:60e63bead773480ead8e98baa4144956
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spelling	oai:doaj.org-article:60e63bead773480ead8e98baa41449562021-11-25T17:30:35ZStill No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds10.3390/e231115291099-4300https://doaj.org/article/60e63bead773480ead8e98baa41449562021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1529https://doaj.org/toc/1099-4300“No free lunch” results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling, which is more or less realistic for a given problem. Some models are “expensive” (strong assumptions, such as sub-Gaussian tails), others are “cheap” (simply finite variance). As it is well known, the more you pay, the more you get: in other words, the most expensive models yield the more interesting bounds. Recent advances in robust statistics have investigated procedures to obtain tight bounds while keeping the cost of assumptions minimal. The present paper explores and exhibits what the limits are for obtaining tight probably approximately correct (PAC)-Bayes bounds in a robust setting for cheap models.Benjamin GuedjLouis PujolMDPI AGarticlestatistical learning theoryPAC-Bayes theoryno free lunch theoremsScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1529, p 1529 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	statistical learning theory PAC-Bayes theory no free lunch theorems Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	statistical learning theory PAC-Bayes theory no free lunch theorems Science Q Astrophysics QB460-466 Physics QC1-999 Benjamin Guedj Louis Pujol Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds
description	“No free lunch” results state the impossibility of obtaining meaningful bounds on the error of a learning algorithm without prior assumptions and modelling, which is more or less realistic for a given problem. Some models are “expensive” (strong assumptions, such as sub-Gaussian tails), others are “cheap” (simply finite variance). As it is well known, the more you pay, the more you get: in other words, the most expensive models yield the more interesting bounds. Recent advances in robust statistics have investigated procedures to obtain tight bounds while keeping the cost of assumptions minimal. The present paper explores and exhibits what the limits are for obtaining tight probably approximately correct (PAC)-Bayes bounds in a robust setting for cheap models.
format	article
author	Benjamin Guedj Louis Pujol
author_facet	Benjamin Guedj Louis Pujol
author_sort	Benjamin Guedj
title	Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds
title_short	Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds
title_full	Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds
title_fullStr	Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds
title_full_unstemmed	Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds
title_sort	still no free lunches: the price to pay for tighter pac-bayes bounds
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/60e63bead773480ead8e98baa4144956
work_keys_str_mv	AT benjaminguedj stillnofreelunchesthepricetopayfortighterpacbayesbounds AT louispujol stillnofreelunchesthepricetopayfortighterpacbayesbounds
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Still No Free Lunches: The Price to Pay for Tighter PAC-Bayes Bounds

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